Solve for $x$ and $y$ using elimination. ${2x-6y = -18}$ ${2x+5y = 26}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-2x+6y = 18}$ $2x+5y = 26$ Add the top and bottom equations together. $11y = 44$ $\dfrac{11y}{{11}} = \dfrac{44}{{11}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {2x-6y = -18}\thinspace$ to find $x$ ${2x - 6}{(4)}{= -18}$ $2x-24 = -18$ $2x-24{+24} = -18{+24}$ $2x = 6$ $\dfrac{2x}{{2}} = \dfrac{6}{{2}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {2x+5y = 26}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(4)}{= 26}$ ${x = 3}$